含分布时滞的时滞微分系统多步龙格-库塔方法的时滞相关稳定性

doi:10.12286/jssx.2019.1.104

计算数学 ›› 2019, Vol. 41 ›› Issue (1): 104-112.DOI: 10.12286/jssx.2019.1.104

• 论文 • 上一篇

含分布时滞的时滞微分系统多步龙格-库塔方法的时滞相关稳定性

丛玉豪^1,2, 胡洋¹, 王艳沛¹

1. 上海大学理学院数学系, 上海 200444;
2. 上海海关学院, 上海 201204

收稿日期:2018-06-16 出版日期:2019-03-15 发布日期:2019-02-18
基金资助:
国家自然科学基金（11471217）资助项目.

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丛玉豪, 胡洋, 王艳沛. 含分布时滞的时滞微分系统多步龙格-库塔方法的时滞相关稳定性[J]. 计算数学, 2019, 41(1): 104-112.

Cong Yuhao, Hu Yang, Wang Yanpei. DELAY-DEPENDENT STABILITY OF MULTISTEP RUNGE-KUTTA METHODS FOR DIFFERENTIAL SYSTEMS WITH DISTRIBUTED DELAYS[J]. Mathematica Numerica Sinica, 2019, 41(1): 104-112.

DELAY-DEPENDENT STABILITY OF MULTISTEP RUNGE-KUTTA METHODS FOR DIFFERENTIAL SYSTEMS WITH DISTRIBUTED DELAYS

Cong Yuhao^1,2, Hu Yang¹, Wang Yanpei¹

1. College of Science, Shanghai University, Shanghai 200444, China;
2. Shanghai Customs College, Shanghai 201204, China

Received:2018-06-16 Online:2019-03-15 Published:2019-02-18

本文研究了一类含分布时滞的时滞微分系统的多步龙格-库塔方法的稳定性.基于辐角原理，本文给出了多步龙格-库塔方法弱时滞相关稳定性的充分条件，并通过数值算例验证了理论结果的有效性.

关键词： 含分布时滞的时滞微分系统, 多步龙格-库塔方法, 弱时滞相关稳定性

This paper is concerned with the stability of multistep Runge-Kutta methods for differential systems with distributed delays. Based on the Argument Principle, a sufficient condition of weak delay-dependent stability of multistep Runge-Kutta methods for the systems is obtained. Furthermore, numerical examples are provided to demonstrate the effectiveness of the theoretical results.

Key words: differential systems with distributed delays, multistep Runge-Kutta methods, weak delay-dependent stability

MR(2010)主题分类:

65L06
65L15

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摘要

含分布时滞的时滞微分系统多步龙格-库塔方法的时滞相关稳定性

DELAY-DEPENDENT STABILITY OF MULTISTEP RUNGE-KUTTA METHODS FOR DIFFERENTIAL SYSTEMS WITH DISTRIBUTED DELAYS

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